I would totally recommend Fox Motel, not only because of its location but also because of the price! I stayed at Fox Motel for 2 weeks and i really enjoyed my stay.
The staff is very friendly: the front desk lady, she doesn't speak english at all, was really nice and helped me with the suitcase. Her husband knows english better and is willing to help if you have any questions about local transport etc.
The room (standart single room) and the bathroom were small but if you plan only to sleep there it's totally fine. The room was very clean. There is no shower curtain, so while taking a shower almost all of the bathroom floor will be flooded.
My room was one of the closest to Juan station rails, so every 10 to 15 minutes at daytime I could hear the Metro Jingles, but I got used to it and by the end of my stay it didn't even bother me anymore and since the last metro runs around midnight it's silent during nighttime.
From Incheon Intl Airport it takes you about 90 minutes by train to get to Juan Station. The travel time to Seoul (central train) Station is approximately 60 to 70 minutes.
There is a little underground shopping mall at Juan Station with various shops like cosmetics, clothes, shoes etc. On the street are different small coffee shops, restaurants and convenience stores, so even though there is no breakfast served at Fox Motel there are different opportunities for breakfast within a few minutes.